Nonconvex quadratic programming (QP) is an NP-hard problem that optimizes a general quadratic function over linear constraints. This paper introduces a new global optimization algorithm for this problem, which combines two ideas from the literature---finite branching based on the first-order KKT conditions and polyhedral-semidefinite relaxations of completely positive (or copositive) programs. Through a series of computational experiments comparing the new algorithm with existing codes on a diverse set of test instances, we demonstrate that the new algorithm is an attractive method for globally solving nonconvex QP.

## Citation

Argonne National Laboratory Mathematics and Computer Science Division Preprint ANL/MCS-P1837-0211

## Article

View Globally Solving Nonconvex Quadratic Programming Problems via Completely Positive Programming